Zobrazeno 1 - 10
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pro vyhledávání: '"Elvetun, Ole Løseth"'
For linear ill-posed problems with nontrivial null spaces, Tikhonov regularization and truncated singular value decomposition (TSVD) typically yield solutions that are close to the minimum norm solution. Such a bias is not always desirable, and we ha
Externí odkaz:
http://arxiv.org/abs/2408.17074
We explore the possibility for using boundary measurements to recover a sparse source term f(x) in the potential equation. Employing weighted sparsity regularization and standard results for subgradients, we derive simple-to-check criteria which assu
Externí odkaz:
http://arxiv.org/abs/2212.04187
We explore the possibility for using boundary data to identify sources in elliptic PDEs. Even though the associated forward operator has a large null space, it turns out that box constraints, combined with weighted sparsity regularization, can enable
Externí odkaz:
http://arxiv.org/abs/2206.06069
This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity regularization does not necessarily produce adequate results for these a
Externí odkaz:
http://arxiv.org/abs/2012.11280
We study whether a modified version of Tikhonov regularization can be used to identify several local sources from Dirichlet boundary data for a prototypical elliptic PDE. This paper extends the results presented in [5]. It turns out that the possibil
Externí odkaz:
http://arxiv.org/abs/2011.04394
We study a source identification problem for a prototypical elliptic PDE from Dirichlet boundary data. This problem is ill-posed, and the involved forward operator has a significant nullspace. Standard Tikhonov regularization yields solutions which a
Externí odkaz:
http://arxiv.org/abs/2005.09444
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Publikováno v:
Mathematics of Computation; Nov2024, Vol. 93 Issue 350, p2811-2836, 26p
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with respect to p
Externí odkaz:
http://arxiv.org/abs/1506.05655
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we study the
Externí odkaz:
http://arxiv.org/abs/1412.5641